In my copending application Ser. No. 277,857, filed Aug. 4, 1972 there is disclosed structure and method relating to spectrography and, more particularly to monochromators employing concave diffraction gratings with fixed entrance and exit slits in which the spectral range of interest is scanned by means of grating rotation. Such application, then, relates to reflective diffraction grating mountings generally similar to the Seya mounting but in contrast thereto being free of the fixed or specific angular constraint which characterizes the Seya mounting and yielding substantially improved optical performance. In fact, said application discloses means by which the angles of incidence and diffraction may be chosen at will to fit the needs and peculiarities of a particular problem. Such a system leads to the capability of providing plural entrance and exit slits, all fixed. The mechanical advantages of such systems are substantial particularly as regards general simplicity and economy resulting therefrom.
However, there are also significant optical advantages which flow from the systems of said application, chief among which are increased resolution and luminosity. Basically, the mountings of said application are characterized by the fact that the sum of the object and image tangential focal length equations is not equated to zero but rather to a value e which is determined as a function of the aberrations produced by the concave grating over the rectangular aperture provided by the ruled area of the grating. The aforesaid application, then, relates to focalization which takes the aberrations into account. Specifically, a change of reference sphere at the exit slit is effected which allows a grating of large width W.sub.o to be used (where W and H represent the retangular coordinates from the center of the grating respectively perpendicular and parallel to the grating lines), in particular wherein the partial derivative of the optical path length P with respect to W is zero, i.e., the total optical path is stationary with respect to W (Fermat's principle).
For spectrometers in which the aberrations are small (i.e. with normal incidence), a computation based upon Strehl's criterion links the image broadening (and therefore the resolution loss) to the amplitudes of the aberrations. For spectrometers in which the aberrations are large (i.e. grazing incidence), the computation is based upon a quality factor characterizing the trace of light rays located in the image plane, weighted by intensity distribution.
The diffraction of the incident spherical wavefront at the rectangular aperture provided by the ruled grating width W.sub.o and height H.sub.o (the width being taken perpendicular to the grating lines) creates a distorted wavefront at the image plane. The difference .DELTA.(w,h) between the distorted wavefront and the reference sphere centered on the Gaussian image is very much greater than the difference .DELTA.'(w,h) between the distorted wavefront and a reference sphere centered on the brightest part of a line at best focus. The change of reference spheres (change of focus) involves a linear term C.sub.1 W and a quadratic term C.sub.2 W.sup.2 relating the two functions .DELTA.(w,h) and .DELTA.'(w,h) as follows: EQU .DELTA.'(w,h) = .DELTA.(w,h) + C.sub.1 W + C.sub.2 (w.sup.2 + h.sup.2)
Two cases must be distinguished:
I. For monochromator mountings in which the deviation of .DELTA.(w,h) over the exit pupil is small with respect to the wavelength .lambda., (i.e. 2.pi..DELTA.(w,h)/.lambda.&lt;&lt;1) the ruled area of grating for a given height H.sub.o thereof and to derive values of C.sub.1 and C.sub.2. These values C.sub.1 and C.sub.2 are then introduced into the grating equation derived from Fermat's principle to obtain a generalized focusing equation in which the main aberration terms (except for astigmatism) are balanced by the defocusing term.
II. For monocromator mountings in which the deviation .alpha.(w,h) is large (2.pi..alpha.(w,h)&gt;&gt;1) the values of C.sub.1 and C.sub.2 in function of the following: ##EQU1## given as equation (1) in my copending application; which requires an initial selection of W.sub.o and H.sub.o and from which Q and consequently the luminosity are deduced.
The case I condition is encountered for in plane mountings operating at "normal" incidence and moderate values of W.sub.o whereas the case II condition is encountered when the aforesaid in plane mountings are required to operate at very high luminosity, requiring large values of W.sub.o (i.e. mountings operating in the VUV region), and for mountings where grazing incidence is used (i.e. operating in the XUV region). It should be noted that whereas for case II the values W.sub.o and H.sub.o are determined at the beginning in order to determine the quality factor and consequently the luminosity, for case I the values W.sub.o and H.sub.o are not chosen initially, being determined on the basis of equation (11) of my copending application. In other words, considering the fundamental focalization equation: ##EQU2## where for case II: ##EQU3## and for case I: ##EQU4## the values W.sub.o and H.sub.o for case II are determined from the following, based upon Strehl's criterion: ##EQU5## whereas for case I W.sub.o and H.sub.o are established initially in consequence of which the quality factor Q and consequently the luminosity are deduced.
In each case, the procedure leads to a residual instrument defocusing the tolerance for which is established in a manner similar to that involved with the depth of focus of conventional optical systems.
That is to say, the mounts according to my copending application are characterised by a residual deviation, the tolerance for which is determined in a manner equivalent to the manner in which the tolerance for depth of focus in classical optical system is determined. Thus, for the case of large aberrations where the quality factor Q is used, one employs the practical limiting resolving power R.sub.p = .lambda./&lt;.delta..lambda.&gt; where &lt;.delta..lambda.&gt; is the limiting resolution and the "instrumental defocusing power" EQU P = .lambda./.delta..lambda.inst
where .delta..lambda.inst is the defect of residual instrumental setting corresponding to the aforesaid residual deviation such that a limiting value ##EQU6## is determined, t being the tolerated depth of focus for the mount equivalent to the tolerable depth of focus employed in classical optical systems. Then EQU .delta..lambda.&lt;t = 1.54.delta..lambda..sub.t
For low aberrations where Strehl's criterion is used and the practical limiting resolving power R.sub.p equals 0.8NW.sub.o K,p must satisfy the condition: ##EQU7## where p in this case equals .lambda./.delta..lambda.t and .delta..lambda.inst.ltoreq.t = 1.54.delta..lambda.t with .delta..lambda..sub.t = .lambda.(0.8NKW.sub.o).sup..sup.-1
Holographic gratings are now available which are efficient in the near and far ultraviolet spectral range and which are produced by photographically recording interference fringes. The development of photochemical processes has enabled such gratings to be obtained with small amounts of diffused light and a high efficiency. Said method of making of gratings has been found to be very flexible since it is possible to control, or to have an action on a plurality of parameters; i.e., the position of the sources which are used to record the grating; the shape of the support for the grating; the shape of the interfering waves.
In acting on these various parameters, it is possible to produce concave gratings with a very large aperture by using a spherical support of large curvature. Moreover, by acting on the position of the sources, certain writers have indicated the possibility of correcting astigmatism. This point is very important especially in the far ultraviolet range where the losses in intensity due to astigmatism are very high.
Prior to the present invention, it was well known that no satisfactory solution to the focusing problem for such gratings existed, compensation for astigmatism resulting in a substantial increase in other aberrations. The only solution which could be envisaged in the case of a mounting with simple rotation of the grating about an axis passing through its top and parallel to the grating lines was a Seya-Namioka type solution for which the angle between the two beams is about 70.degree.15. Even in this case, the aberrations are greater in the case of such gratings than in classical gratings. From the practical point of view these gratings could have a great advantage by obtaining extensive ruled surfaces with a high number of lines per millimeter by using the general focusing principles described in my copending application. It is to be recalled that contrary to generally accepted focusing principles, my copending application considers that the equations of Fermat's principle must be satisfied as a whole, that is, the first term must not merely be considered zero, but on the contrary, the sum of the terms must be cancelled. In other words, instead of considering the sum T + T' of the equations of the object and image tangential focal lengths as zero which brings about an evaluation of aberrations with respect to an image point corresponding to the limiting case of a zero aperture, a phase compensation method is used by displacement of the reference sphere and the aberrations are evaluated with respect to the brightest point of the image. Owing to the generally high value of the coefficients of aberration, and thus on account of the high value of the ruled surface particularly in the case of holographic gratings, the amplitudes of the aberrations vary rapidly with the position of the reference image plane, i.e., the plane wherefrom one observes the structure of the image of the object slot given by the grating. Further, although it is conventional to employ a purely mathematical method of the function f = T + T' so as to obtain the parameters necessary for solving the equation T + T' = 0 in the case of a particular mounting, a more physical method is disclosed in my copending application. Namely, in order for image formation to take place, the derivative of the optical path must be zero, whereby the equations which are derived from this principle must be satisfied regardless of wavelength. It is therefore necessary to consider the focusing relationship of the second order, i.e. that which takes into account a compensation of the aberrations by an appropriate selection of the image plane, which best satisfies the spectral range of utilisation.